E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
I could brain him with his ladys fan (1 Henry IV., ii. 3)i.e. knock his brains out with a fan handle. The ancient fans had long handles, so that ladies used their fans for walking-sticks, and it was by no means unusual for very testy dames to chastise unruly children by beating them with their fansticks.